相关论文: Active Learning for Neural PDE Solvers

Pool-based active learning (AL) is a promising technology for increasing data-efficiency of machine learning models. However, surveys show that performance of recent AL methods is very sensitive to the choice of dataset and training…

A major problem with Active Learning (AL) is high training costs since models are typically retrained from scratch after every query round. We start by demonstrating that standard AL on neural networks with warm starting fails, both to…

Many Partial Differential Equations (PDEs) do not have analytical solution, and can only be solved by numerical methods. In this context, Physics-Informed Neural Networks (PINN) have become important in the last decades, since it uses a…

Solving partial differential equations (PDEs) on shapes underpins many shape analysis and engineering tasks; yet, prevailing PDE solvers operate on polygonal/triangle meshes while modern 3D assets increasingly live as neural…

While deep learning (DL) is data-hungry and usually relies on extensive labeled data to deliver good performance, Active Learning (AL) reduces labeling costs by selecting a small proportion of samples from unlabeled data for labeling and…

Partial differential equations (PDEs) are central to modeling physical and engineering systems, but repeatedly solving parametric PDEs remains computationally expensive. Operator learning enables fast surrogate inference, yet typically…

The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions. Related learning problems are often stated as variational formulations…

Active learning (AL) is a learning paradigm where an active learner has to train a model (e.g., a classifier) which is in principal trained in a supervised way, but in AL it has to be done by means of a data set with initially unlabeled…

Scientific machine learning is an emerging field that broadly describes the combination of scientific computing and machine learning to address challenges in science and engineering. Within the context of differential equations, this has…

Active learning (AL) is a subfield of machine learning (ML) in which a learning algorithm could achieve good accuracy with less training samples by interactively querying a user/oracle to label new data points. Pool-based AL is…

Partial differential equations (PDEs) underpin the modeling of many natural and engineered systems. It can be convenient to express such models as neural PDEs rather than using traditional numerical PDE solvers by replacing part or all of…

Active Learning (AL) has emerged as a powerful approach for minimizing labeling costs by selectively sampling the most informative data for neural network model development. Effective AL for large-scale vision-language models necessitates…

PDEs are central to scientific and engineering modeling, yet designing accurate numerical solvers typically requires substantial mathematical expertise and manual tuning. Recent neural network-based approaches improve flexibility but often…

We propose a trainable-by-parts surrogate model for solving forward and inverse parameterized nonlinear partial differential equations. Like several other surrogate and operator learning models, the proposed approach employs an encoder to…

Active learning (AL) aims to improve model performance within a fixed labeling budget by choosing the most informative data points to label. Existing AL focuses on the single-domain setting, where all data come from the same domain (e.g.,…

Artificial intelligence is transforming scientific computing with deep neural network surrogates that approximate solutions to partial differential equations (PDEs). Traditional off-line training methods face issues with storage and I/O…

We propose Physics-Aware Neural Implicit Solvers (PANIS), a novel, data-driven framework for learning surrogates for parametrized Partial Differential Equations (PDEs). It consists of a probabilistic, learning objective in which weighted…

Active Learning (AL) addresses the crucial challenge of enabling machines to efficiently gather labeled examples through strategic queries. Among the many AL strategies, Uncertainty Sampling (US) stands out as one of the most widely…

We introduce a practical method to enforce partial differential equation (PDE) constraints for functions defined by neural networks (NNs), with a high degree of accuracy and up to a desired tolerance. We develop a differentiable…

Neural networks have promise as surrogate partial differential equation (PDE) solvers, but it remains a challenge to use these concepts to solve problems with high accuracy and scalability. In this work, we show that neural network…